Horizon Formation in High-Energy Particles Collision

We investigate a classical formation of a trapped surface in 4-dimensional flat space-time in a process of a non-head-on collision of two high-energy particles which are treated as Aichelburg-Sexl shock waves. From the condition of the horizon volume local maximality an equation for the trapped surface is deduced. Using a known solution on the shocks we find a time-dependent solution describing the trapped surface between the shocks. We analyze the horizon appearance and evolution. Obtained results may describe qualitatively the horizon formation in higher dimensional space-time.Comment: Latex2e, 8 pages, 6 figures, references adde

Non-linear spectroscopy of rubidium: An undergraduate experiment

In this paper, we describe two complementary non-linear spectroscopy methods which both allow to achieve Doppler-free spectra of atomic gases. First, saturated absorption spectroscopy is used to investigate the structure of the $5{\rm S}_{1/2}\to 5{\rm P}_{3/2}$ transition in rubidium. Using a slightly modified experimental setup, Doppler-free two-photon absorption spectroscopy is then performed on the $5{\rm S}_{1/2}\to 5{\rm D}_{5/2}$ transition in rubidium, leading to accurate measurements of the hyperfine structure of the $5{\rm D}_{5/2}$ energy level. In addition, electric dipole selection rules of the two-photon transition are investigated, first by modifying the polarization of the excitation laser, and then by measuring two-photon absorption spectra when a magnetic field is applied close to the rubidium vapor. All experiments are performed with the same grating-feedback laser diode, providing an opportunity to compare different high resolution spectroscopy methods using a single experimental setup. Such experiments may acquaint students with quantum mechanics selection rules, atomic spectra and Zeeman effect.Comment: 16 pages, 8 figure

Энергетические, экономические и экологические показатели энергоэффективности

У статті розглянута проблема ефективного використання енергетичних ресурсів в Україні. Визначені питання підвищення енергетичної ефективності, представлені основні показники енергоефективності в промисловості для простого технологічного процесу, виробничої одиниці та підприємства вцілому. Наведені основні методи підвищення енергоефективності. Проаналізовано необхідність застосування трьох систем показників: енергетичних, економічних, екологічних, що вважається достатнім для всебічної оцінки ефективності нововведень.In the article is considered the problem of energy efficiency in Ukraine. Questions of increase of energy efficiency are identified. Represented the main indicators of energy efficiency in the industry for a simple process, production units and the enterprise as a whole. Resulted main methods of increasing energy efficiency. The analysis of the need for the three indicators: energy, economic, environmental, considered sufficient to assess the effectiveness of comprehensive innovation.В статье рассмотрена проблема эффективного использования энергетических ресурсов в Украине. Определены вопросы повышения энергетической эффективности, представленны оснвные показатели энергоэффективности в промышленности для простого технологического процесса, производственной единицы и предприятия в целом. Приведены основные методы повышения энергоэффективности. Проанализирована необходимость применения трех систем показателей: энергетических, экономических, экологических, что является достаточным для всесторонней оценки эффективности нововведений

New results on group classification of nonlinear diffusion-convection equations

Using a new method and additional (conditional and partial) equivalence transformations, we performed group classification in a class of variable coefficient $(1+1)$-dimensional nonlinear diffusion-convection equations of the general form $f(x)u_t=(D(u)u_x)_x+K(u)u_x.$ We obtain new interesting cases of such equations with the density $f$ localized in space, which have large invariance algebra. Exact solutions of these equations are constructed. We also consider the problem of investigation of the possible local trasformations for an arbitrary pair of equations from the class under consideration, i.e. of describing all the possible partial equivalence transformations in this class.Comment: LaTeX2e, 19 page

Reduction Operators of Linear Second-Order Parabolic Equations

The reduction operators, i.e., the operators of nonclassical (conditional) symmetry, of (1+1)-dimensional second order linear parabolic partial differential equations and all the possible reductions of these equations to ordinary differential ones are exhaustively described. This problem proves to be equivalent, in some sense, to solving the initial equations. The ``no-go'' result is extended to the investigation of point transformations (admissible transformations, equivalence transformations, Lie symmetries) and Lie reductions of the determining equations for the nonclassical symmetries. Transformations linearizing the determining equations are obtained in the general case and under different additional constraints. A nontrivial example illustrating applications of reduction operators to finding exact solutions of equations from the class under consideration is presented. An observed connection between reduction operators and Darboux transformations is discussed.Comment: 31 pages, minor misprints are correcte

Resonant nonlinear magneto-optical effects in atoms

In this article, we review the history, current status, physical mechanisms, experimental methods, and applications of nonlinear magneto-optical effects in atomic vapors. We begin by describing the pioneering work of Macaluso and Corbino over a century ago on linear magneto-optical effects (in which the properties of the medium do not depend on the light power) in the vicinity of atomic resonances, and contrast these effects with various nonlinear magneto-optical phenomena that have been studied both theoretically and experimentally since the late 1960s. In recent years, the field of nonlinear magneto-optics has experienced a revival of interest that has led to a number of developments, including the observation of ultra-narrow (1-Hz) magneto-optical resonances, applications in sensitive magnetometry, nonlinear magneto-optical tomography, and the possibility of a search for parity- and time-reversal-invariance violation in atoms.Comment: 51 pages, 23 figures, to appear in Rev. Mod. Phys. in Oct. 2002, Figure added, typos corrected, text edited for clarit

The level of air pollution in the impact zone of coal-fired power plant (Karaganda City) using the data of geochemical snow survey (Republic of Kazakhstan)

Coal-fired power plants emissions impact the air quality and human health. Of great significance is assessment of solid airborne particles emissions from those plants and distance of their transportation. The article presents the results of air pollution assessment in the zone of coal-fired power plant (Karaganda City) using snow survey. Based on the mass of solid airborne particles deposited in snow, time of their deposition on snow at the distance from 0.5 to 4.5 km a value of dust load has been determined. It is stated that very high level of pollution is observed at the distance from 0.5 to 1 km. there is a trend in decrease of dust burden value with the distance from the stacks of coal-fired power plant that may be conditioned by the particle size and washing out smaller ash particles by ice pellets forming at freezing water vapour in stacks of the coal-fired power plant. Study in composition of solid airborne particles deposited in snow has shown that they mainly contain particulates of underburnt coal, Al-Si- rich spheres, Fe-rich spheres, and coal dust. The content of the particles in samples decreases with the distance from the stacks of the coal-fired power plant

Digital receivers for low-frequency radio telescopes UTR-2, URAN, GURT

This paper describes digital radio astronomical receivers used for decameter and meter wavelength observations. This paper describes digital radio astronomical receivers used for decameter and meter wavelength observations. Since 1998, digital receivers performing on-the-fly dynamic spectrum calculations or waveform data recording without data loss have been used at the UTR-2 radio telescope, the URAN VLBI system, and the GURT new generation radio telescope. Here we detail these receivers developed for operation in the strong interference environment that prevails in the decameter wavelength range. Data collected with these receivers allowed us to discover numerous radio astronomical objects and phenomena at low frequencies, a summary of which is also presented.Comment: 24 pages, 15 figure